Abstract
The action of various one-dimensional integral operators, discretized by a suitable quadrature method, can be compressed and accelerated by means of Chebyshev series approximation. Our approach has a different conception with respect to other well-known fast methods: its effectiveness rests on the “smoothing effect” of integration, and it works in linear as well as nonlinear instances, with both smooth and nonsmooth kernels. We describe a Matlab toolbox which implements Chebyshev-like compression of discrete integral operators, and we present several numerical tests, where the basic O(n 2) complexity is shown to be reduced to O(mn), with m≪n.
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De Marchi, S., Vianello, M. Approximating the Approximant: A Numerical Code for Polynomial Compression of Discrete Integral Operators. Numerical Algorithms 28, 101–116 (2001). https://doi.org/10.1023/A:1014030412645
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DOI: https://doi.org/10.1023/A:1014030412645